Learning new skills or knowledge traditionally involves lectures, where an instructor spends a majority of time presenting materials to the participants in an activity. The instructor is primarily responsible for pacing the activity and setting the level of rigor. Participant involvement, unfortunately, tends to be limited to asking questions when confusion arises. Such one-way communication discourages critical thinking and has been shown to do little in improving the participants' understanding of the concepts presented.
Various teaching methods in which participants actively discuss new material among themselves encourage engagement and allow the participants to cooperatively reach consensus on correct answers, which results in a deeper understanding of new material. Such cooperative learning methods including, for example, “peer instruction” and “think-pair-share,” generally require appropriately grouping the participants so as to foster a positive and meaningful discussion in each group. See, e.g., Crouch & Mazur, “Peer Instruction: Ten years of experience and results,” American Journal of Physics, 69(9), 970. (2001); E. Mazur, Peer Instruction: A User's Manual. (1997); Cooper & Robinson, “Getting Started: Informal Small-Group Strategies in Large Classes” New directions for teaching and learning, 81, 17-24. (2000).
Conventionally, the instructor or organizer allows participants to self-select into groups; this is especially common in large activities or when groups are arranged based on the spatial locations of the participants. As a result, some participants are grouped with others who have comparable knowledge, the same misconception, or the same correct understanding; this reduces learning opportunities through productive conversations within the group. A “productive conversation” as used herein means one in which each participant in the group gains from the discussion experience, such as switching from the wrong answer to the correct answer, improving his or her understanding of the correct answer, or developing a greater understanding of why the wrong answers are in fact wrong. Grouping the participants randomly or with an unplanned approach may produce productive conversations only by chance, thereby greatly hampering the potential and effectiveness of the cooperative learning approaches.
Consequently, there is a need for an approach that groups participants in an activity with a substantially high likelihood of producing productive conversations in each group.